Essential annuli in genus two handlebody exteriors
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914742328623104 |
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| author | Koda, Yuya Ozawa, Makoto Wang, Yi-Sheng |
| author_facet | Koda, Yuya Ozawa, Makoto Wang, Yi-Sheng |
| contents | We classify all potential configurations of essential annuli in a genus two atoroidal handlebody exterior in the $3$-sphere, building on two recent classifications: the classification of the JSJ-graph of the exterior and the classification of essential annuli in the exterior. In contrast to knots, genus two handlebody exteriors may contain infinitely many non-isotopic essential annuli, due to the JSJ-graph classification. Our main result characterizes the numbers of different types of essential annuli in such an infinite family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Essential annuli in genus two handlebody exteriors Koda, Yuya Ozawa, Makoto Wang, Yi-Sheng Geometric Topology 57M50 (Primary) 57M15, 57K12 (Secondary) We classify all potential configurations of essential annuli in a genus two atoroidal handlebody exterior in the $3$-sphere, building on two recent classifications: the classification of the JSJ-graph of the exterior and the classification of essential annuli in the exterior. In contrast to knots, genus two handlebody exteriors may contain infinitely many non-isotopic essential annuli, due to the JSJ-graph classification. Our main result characterizes the numbers of different types of essential annuli in such an infinite family. |
| title | Essential annuli in genus two handlebody exteriors |
| topic | Geometric Topology 57M50 (Primary) 57M15, 57K12 (Secondary) |
| url | https://arxiv.org/abs/2404.04503 |